Shryia read a $481$ -page-long book cover to cover in a single session, at a constant rate. After reading for $1.5$ hours, she had $403$ pages left to read. How fast was Shryia reading?
Solution: Let's say that Shryia was reading at a rate of $V$ pages per hour. Then, she read $V\cdot T$ pages in $T$ hours. In addition, we know that she had $481$ pages to read in total. The total number of pages is comprised of the number of pages Shryia had already read and the number of pages that remained. We can express this with the equation $481=V\cdot T+R$, where: $V$ represents Shryia's reading speed (in pages per hour) $T$ represents the time (in hours) $R$ represents the number of remaining pages to read at a given time We know that after $1.5$ hours $(T={1.5})$, Shryia had $403$ pages left to read $(R={403})$. Let's plug these values into the equation to find the value of $V$. $ \begin{aligned}481&=V\cdot{1.5}+{403}\\ 1.5V&=78\\ V&=52\end{aligned}$ Therefore, Shryia was reading at a rate of $52$ pages per hour. To find how long it took Shryia to finish the entire book, we can plug $R=0$ into the equation and solve for $T$. $ \begin{aligned}481&=52T+0\\ 52T&=481\\ T&=9.25\end{aligned}$ Shryia was reading at a rate of $52$ pages per hour. It took Shryia $9.25$ hours to finish the entire book.